RMO Practice question 4

Algebra Level 4

(2λ3μ)2+(24λ+3μ)2+(2λ3)2+40312η \sqrt{(2\lambda-3\mu)^{2}+ (2-4\lambda+3\mu)^{2}+(2\lambda-3)^{2}+4031^{2}} \geq \eta

Find the maximum integer value of η \eta , such that for all real numbers λ,μ\lambda,\mu, the inequality above is fulfilled.

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